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Knuth D.E. — The art of computer programming (Vol. 2. Seminumerical algorithms)
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Íàçâàíèå: The art of computer programming (Vol. 2. Seminumerical algorithms)Àâòîð: Knuth D.E. Àííîòàöèÿ: This multivolume work on the analysis of algorithms has long been recognized as the definitive description of classical computer science. The three complete volumes published to date already comprise a unique and invaluable resource in programming theory and practice. Countless readers have spoken about the profound personal influence of Knuth's writings. Scientists have marveled at the beauty and elegance of his analysis, while practicing programmers have successfully applied his "cookbook" solutions to their day-to-day problems. All have admired Knuth for the breadth, clarity, accuracy, and good humor found in his books. To begin the fourth and later volumes of the set, and to update parts of the existing three, Knuth has created a series of small books called fascicles, which will be published at regular intervals. Each fascicle will encompass a section or more of wholly new or revised material. Ultimately, the content of these fascicles will be rolled up into the comprehensive, final versions of each volume, and the enormous undertaking that began in 1962 will be complete. Volume 4, Fascicle 2 - This fascicle inaugurates the eagerly awaited publication of Knuth's "The Art of Co
ßçûê: Ðóáðèêà: Computer science /Àëãîðèòìû /Ñòàòóñ ïðåäìåòíîãî óêàçàòåëÿ: Ãîòîâ óêàçàòåëü ñ íîìåðàìè ñòðàíèö ed2k: ed2k stats Èçäàíèå: 2nd editionÃîä èçäàíèÿ: 1981Êîëè÷åñòâî ñòðàíèö: 688Äîáàâëåíà â êàòàëîã: 18.11.2005Îïåðàöèè: Ïîëîæèòü íà ïîëêó |
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Continued fractions, with polynomial quotients 420 479 500 Continuous binomial distribution 553 Continuous distribution function 47 51 55 58 116—117 576 Continuous Poisson distribution 552 Convergents 363 380 420 Conversion of representations 205 208—209 212 237 273—274 277 287—289 301 see Convolution 290 385 535 551 Convolution, cyclic 290—294 300 491—494 502—503 Convolution, multidimensional 651 Convolution, negacyclic 503 Conway, John Horton 385 Cook, Stephen Arthur vi 195 280 296 301 617 648 Cook, Stephen Arthur, multiplication algorithm 280—285 617 Cooley, James William 642 Coolidge, Julian Lowell 467 Coonen, Jerome 210 Copeland, Arthur Herbert 165 Coppersmith, Don 168 169 482 Coroutine 360 610 Correlation coefficient 70—75 78—85 127 Cosine 231 471 Couffignal, Louis 186 Counting law 636 Coupon collector's test 61—63 74 151 167 Covariance 134 Coveyou, Robert Reginald 26 34 84 88 110 527 Cox, Albert George 263 Craps 174 CRAY-I 391 Cryptanalysis 177 386—389 397 486 Cusick, Thomas William 548 Cycle in a sequence 7—9 21 34—36 Cycle in a sequence, detection of 4 7—8 Cyclic convolution 290—294 300 491—494 502—503 Cyclotomic polynomials 378 432—433 440 492 496 Dahl, Ole-Johan 141 Darling, Donald Allan 56 Datta, Bibhutibhusan 441 Davenport, Harold 359 Davis, Chandler 564 Davis, Clive Selwyn 603 de Bruijn, Nicolaas Govert 196 605 614 629 636 de Bruijn, Nicolaas Govert, cycle 35—36 de Groote, Hans Friedrich 648 de Jong, Lieuwe Sytse 497 de Jonquieres, Adm. Jean Philippe Ernest de Fauque 445 449 458 de la Vallee Poussin, Charles Louis Xavier Joseph 366 Debugging 205—207 260—261 314 656 DEC 20 14 Decimal computer: a computer that manipulates numbers primarily in the decimal (radix ten) number system 186 Decimal digits 179 302 Decimal fractions 181—182 Decimal number system 181—183 194—195 359 decimal point 179 182 Decision, unbiased 2 114—116 122 134 Decuple-precision floating point 268 Dedekind, Richard 78 Dedekind, Richard, sum 78—87 104 Definitely greater than 208 218 228 Definitely less than 208 218 228 Definition of randomness 2 142—169 Degree of a polynomial 399 401 418 Degrees of freedom 41—42 476—477 499—500 Dekker, Theodorus Jozef 227 229 237 Dellac, H. 445 Density function 119—120 134 Dependence 127 134 see Dependence, algebraic 499 Dependence, linear 381 423 425—427 610 Derivative 421 470 507 631 Descartes, Rene 391 Determinant 338 358 415 416 479—480 482 496 Dewey, Melvil, notation for trees 530 Diaconis, Persi Warren 248 249 578 Diamond, Harold George 230 Dice 2 6 39—42 56 115—116 174 Dickman, Karl 367 Dickson, Leonard Eugene 271 371 376 598 Dieter, Ulrich Otto vii 85 87 98 110 114 124—125 129 132 133 553 Differences 281—282 484—487 498 Differentiation see “Derivative” Digit, binary 179 184 Digit, decimal 179 302 Digit, hexadecimal 179 185 194 Digit, octal 185 194 Dilogarithm 578 Dime, Bailey Whitfield 388 Diophantine equations 326—327 337 359 Direct product 502 504 505 Direct sum 502 504 505 Directed graph 460—462 466 Dirichlet, Peter Gustav Lejeune- 637 Discrepancy 37 105—110 113 Discrete distribution function 45 115—116 131—141 Discrete Fourier Transform 290—294 300 482—484 487 494 497 502—503 Discriminant of a polynomial 619 628 632 Distinct-degree factorization 429—431 439 632 Distribution functions 45—47 51 116—117 135 241—242 247 345—346 Distribution functions, continuous 47 51 55 58 116—117 576 Distribution functions, discrete 45 115—116 131—141 Distribution functions, empirical 47—50 Distribution functions, mixture of 118—119 133—134 Distribution functions, product of 116—117 Distribution, Beta 129—131 Distribution, binomial 131—133 136 160 385 531 553 Distribution, chi-square 41 45 47 65 130 Distribution, discrete 45 115—116 131—141 Distribution, exponential 114 128—133 554 Distribution, F- 130 Distribution, gamma 129—130 135 Distribution, geometric 131 132 135 535 549 551 Distribution, integer-valued 131—135 Distribution, Kolmogorov — Smirnov 48—49 55—56 58 Distribution, mixture 118—119 133—134 Distribution, negative binomial 135 Distribution, normal 54 71 117—127 129 130 134—135 368 Distribution, of floating point numbers 238—249 Distribution, of leading digits 239—249 Distribution, of prime factors 367—369 395 Distribution, of prime numbers 366—367 396 616 632—633 Distribution, partial quotients of continued fraction 345—353 615—616 Distribution, Poisson 53 132—133 135—136 517 Distribution, Student's 130 Distribution, t- 130 Distribution, tail of binomial 160 Distribution, tail of normal 122—123 134 Distribution, uniform 2 9 45 47 55 114 116—120 133 248 Distribution, variance-ratio 130 Distribution, wedge-shaped 120—121 Distribution: A specification of probabilities that govern the value of a random variable 2 114 116 Distributive laws 215—216 229 317 399 636 Divide-and-correct 255—260 263—268 Divided differences 485 498 Division 178 250—251 255—260 263—268 295—297 Division, complex 212 268 647 Division, continued fractions 602 Division, double-precision 235—237 division, floating point 204—205 208 212 215 224 226 228—230 235—237 248 577 Division, fractions 313 315 Division, long 255—260 263—268 Division, mixed-radix 193 589 Division, mod m 25 (exercise 7) 277 337 427—428 480 Division, modular 277 Division, multiple-precision 255—261 263—268 295—297 Division, polynomial 401—420 468—469 515 Division, power series 506—507 514—515 Division, pseudo- 407—409 416 418 Division, string polynomials 418 Division, synthetic 402 Divisor, polynomial 403 Dixon, John Douglas 356 385 395 397 Dixon, Wilfrid Joseph 71 Dobell, Alan Rodney 16 Dobkin, David Paul 638 652 Donsker, Monroe David 532 Doob, Joseph Leo 532 Dorn, William Schroeder 469 Double-precision arithmetic 230—237 263—264 278—279 Doubling 305 360 443 Doubling step 447 Downey, Peter James 466 Dragon curve 564 566 607 Dresden, Arnold 180 Drift 221—222 229—230 Dual of an addition chain 462 466 639 Duncan, Robert Lee 249 Duodecimal number system 183 Dupre, Athanase 605 Durbin, James 54 Durham, Stephen Daniel 32 Durstenfeld, Richard 140 e 11 73 342 360 659—660 666 Earle, John Goodell 296 Easton, Malcolm Coleman 555 EDVAC 210 Effective algorithms 154—156 164—166 169 Egyptian mathematics 318 443 Eisenstein, Ferdinand Gotthold 438 Electrologica X8 206 Ellipse, random point on 130—131 136 Ellipse, volume of 101 Empirical distribution function 47—50 Empirical tests for randomness 59—75 Encoding a permutation 64 75 139 Encoding secret messages 177 386—389 397 486 Engineering Research Associates 192 ENIAC 52 Enison, Richard Lawrence 30 Enumeration of tree structures 639 Equality, approximate 208 217—219 228—229 Equidistributed sequence 143—145 157 166—169 Equidistribution test 59 72 Equivalent addition chains 461 466 Eratosthenes, sieve of 394 Erdos, Pal (= Paul) 369 451 638 ERH see “GRH” ERNIE 3 Error estimation 206 213 216—217 237 240 293—294 Error, relative 206 213 216—217 237 240 Essential equality 218—219 228—229 Estrin, Gerald 469 Euclid's Algorithm 81—83 113 272 289 317—320 323—324 338—339 544 Euclid's algorithm, analysis of 339—364 605 Euclid's algorithm, extended 325 337 417 515 Euclid's algorithm, for polynomials 405—420 515 Euclid's algorithm, for string polynomials 419 Euclid's algorithm, multiple-precision 327—330 Euclides (= Euclid) 318—320 Eudoxus of Cnidus 318 342 Euler, constant 342 360 611 629 659—660 666 Euler, Leonhard 340 360 361 391 602 Euler, theorem 19 270 273 523 Euler, totient function 19 273 353—354 361 548 666 Evaluation, of mean and standard deviation 216 229 Evaluation, of monomials 465—466 Evaluation, of polynomials 466—505 588 Evaluation, of powers 441—466 Evaluation: Computing the value, of determinants 416 479—480 482 Eve, James 474 499 Eventually periodic sequence 7—8 21 359 369—371 Excess q exponent 198—199 211 231 Exclusive OR 29—31 177 400 Exercises, notes on ix—xi Exhaustive search 99—100 Exponent overflow 201 203 206 211 216 227—228 233 Exponent part of a floating point number 198—199 231 248 268 Exponent underflow 201 203 206 211 216 227—228 233 Exponential deviate, generating 128 Exponential distribution 114 128—133 554 Exponential function 297 471 514 Exponential sums 79—81 105—109 113 168 366 Exponentiation: Raising to a power 441—466 507 656 Extended arithmetic 230 593 Extended Euclidean algorithm 325 337 417 515 F-distribution 130 Factor method of exponentiation 443 445 462—463 466 Factorial number system 64 192 Factorial power 281—282 497 597 664 Factorization, of polynomials 420—441 Factorization, uniqueness of 403—404 417 Factorization: Discovering factors, of integers 12—13 317 353 364—398 464 FADD (floating add) 208 209 211 498 Fan, Chung Teh 137 Farmwald, Paul Michael 190 Fast Fourier Transform 71 290—294 300 483—484 486 494 497 651 653 Fateman, Richard J 443 FCMP (floating compare) 208 229 FDIV (floating divide) 208 Fermat, numbers 13 371 375 380 Fermat, Pierre de 371—372 375 391 544 Fermat, theorem 375 394 421 FFT see “Fast Fourier transform” Fibonacci, Leonardo, of Pisa 181 192 265 Fibonacci, number system 193 Fibonacci, numbers, table 661 Fibonacci, numbers: elements of the Fibonacci sequence 664 Fibonacci, sequence 26 28 33 34 44 50 52 88 343 172 448 464 568 611 616 Field, finite 28 438 529 630 643 Field: An algebraic system admitting addition, subtraction, multiplication, and division 197 314 401—403 487 506 Fike, Charles Theodore 472 Finite Fourier transform see “Discrete Fourier transform” Finite sequence, random 145 161—164 Fischer, Michael John, vii 301 Fischer, Patrick Carl 226 fix 208 Fix-to-float conversion 205 208 Fixed point arithmetic 193 198 292—294 Fixed slash 314—315 363—364 Flat distribution see “Uniform distribution” Flehinger, Betty Jeanne 247 Fletcher, William 654 Float-to-fix conversion 208 209 212 Floating binary numbers 198 210—212 238—239 248 Floating decimal numbers 198 210—211 238—239 Floating hexadecimal numbers 238—239 248 Floating point arithmetic 33 172 180 198—249 276 314 530 Floating point arithmetic, accuracy of 206 213—230 237 311—312 420 466—467 Floating point arithmetic, addition 199—204 209 211—216 219—230 232—234 237 238—239 249 Floating point arithmetic, axioms 214—218 227—229 Floating point arithmetic, comparison 208 217—219 224 227—229 Floating point arithmetic, decuple-precision 268 Floating point arithmetic, division 204—205 208 212 215 224 226 228—230 235—237 248 577 Floating point arithmetic, double-precision 230—237 263—264 Floating point arithmetic, interval 212 225—227 230 570 Floating point arithmetic, mod 212 228 Floating point arithmetic, multiplication 204 207 208 215—216 224 226—230 234—235 237 248—249 Floating point arithmetic, operators of MIX 208 211 498 Floating point arithmetic, reciprocal 228 248 Floating point arithmetic, remainder 212 228 Floating point arithmetic, single-precision 198—213 Floating point arithmetic, subtraction 200—204 214—216 219—225 230 232—234 238—239 249 Floating point arithmetic, summation 216 229 Floating point arithmetic, triple-precision 237 Floating point arithmetic, unnormalized 223—225 227 229 310 Floating point numbers 180 198—199 206 223 225 231 Floating point numbers, radix b, excess q 198—199 Floating point numbers, statistical distribution 238—249 Floating point radix conversion 309—312 Floating point trigonometric subroutines 231 471 Floating slash 314—316 363
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